10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

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n ( S ) = 12 C 4 ​ × 8 C 4 ​ × 4 C 4 ​ × 3 ! n ( E ) = the number of ways in which one boy gets both the pens = 10 C 2 ​ × 8 C 4 ​ × 4 C 4 ​ × ( 3 !) ∴ P ( E ) = 1 − 12 C 4 ​ × 8 C 4 ​ × 4 C 4 ​ 3 ! 10 C 2 ​ × 8 C 4 ​ × 4 C 4 ​ × ( 3 !) ​ = 1 − 11 1 ​ = 11 10 ​

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